What is Domain Authority?
1. Improve SEO
As I've already told in above that DA is an important factor in SEO. So, you need to improve your website or blog's overall SEO, and that includes all the on page and off page stuff such as website structure, sitemaps, meta tags, original content, social bookmarking, classified ads, guest blogging, URL structure, breadcrumbs, keywords, alt tags, and so on.
2. Unique Content
Unique content is the key of success in blogging profession. But its not enough to write only useful content for your readers. I know that your readers always share your content on their social media profiles. But they never link to your content. So try to write some more unique linkable content. For example: If you have developed any widget then definitely if people will share the widget code on their blogs then they will link to your original code.
That's what I want to say to you. Now, its depend on your what type of content you want to publish on your blogs.
Bloggers are crazy for backlinks. But they give less importance to internal linking. Although internal linking is much beneficial for your readers and search engines that crawl and index your blog. Recently I have visited one blog (viralscape.com), only 75 backlinks and 33,252 worldwide alexa. They are using internal linking and social media technique to promote new/old blog posts.
4. Clean up Low Quality Links
Please clean up low quality spammy links from your website. They can be play a great role to harm your website. If there are so many bad links then make a time table to clean 10-20 spammy links. I have undergone through Google's manual action penalty.
5. Patience is the key
Old Age domains are getting higher DA. It takes time to build the domain authority. If you're working on your blog or website in the right way, you should see your DA increase slowly. It all doesn't happen within a hours or day.
Better quality content means lot of sharing. Huge sharing means good traffic and traffic can provide you some backlinks so your DA will be increase dramatically. Good Luck :)